study the table.\n| x | y |\n| -2 | 8 |\n| -1 | 2 |\n| 0 | 0 |\n| 1 | 2 |\n| 2 | 8 |\nwhich best describes…

study the table.\n| x | y |\n| -2 | 8 |\n| -1 | 2 |\n| 0 | 0 |\n| 1 | 2 |\n| 2 | 8 |\nwhich best describes the function represented by the data in the table?\nlinear with a common ratio of 4\nlinear with a common second difference of 4\nquadratic with a common second difference of 4

study the table.\n| x | y |\n| -2 | 8 |\n| -1 | 2 |\n| 0 | 0 |\n| 1 | 2 |\n| 2 | 8 |\nwhich best describes the function represented by the data in the table?\nlinear with a common ratio of 4\nlinear with a common second difference of 4\nquadratic with a common second difference of 4

Answer

Explanation:

Step1: Check for linear - common difference

Find the first - differences of (y) values. When (x=-2,y = 8); when (x=-1,y = 2), the difference is (2 - 8=-6). When (x=-1,y = 2); when (x = 0,y = 0), the difference is (0 - 2=-2). Since the first - differences are not constant, it is not a linear function.

Step2: Calculate first - differences

Let (y_1 = 8,y_2 = 2,y_3 = 0,y_4 = 2,y_5 = 8). The first - differences are (\Delta y_1=y_2 - y_1=2 - 8=-6), (\Delta y_2=y_3 - y_2=0 - 2=-2), (\Delta y_3=y_4 - y_3=2 - 0 = 2), (\Delta y_4=y_5 - y_4=8 - 2 = 6).

Step3: Calculate second - differences

The second - differences are (\Delta^2y_1=\Delta y_2-\Delta y_1=-2-(-6)=4), (\Delta^2y_2=\Delta y_3-\Delta y_2=2-(-2)=4), (\Delta^2y_3=\Delta y_4-\Delta y_3=6 - 2=4). Since the second - differences are constant ((4)), the function is quadratic.

Answer:

quadratic with a common second difference of 4